The Haskell Road to Logic, Maths and Programming. Second edition

by Kees Doets, Van Jan Eijck

Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply There is no royal road to mathematics. Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: Doets and van Eijck s The Haskell Road to Logic, Maths and Programming is an astonishingly extensive and accessible textbook on logic, maths, and Haskell. Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau

Genres: Programming, Computer Science, Mathematics, Computers, Logic, Science, Nonfiction

450 pages, Paperback

First published May 7, 2004

Reviews

[Nick Black · Rating 4 out of 5]

freakin' awesome!

[Catalin Marin · Rating 5 out of 5]

An exceptional book for learning both logic and Haskell

[Jon Gauthier · Rating 3 out of 5]

Without a doubt, the math contents of this book were over my head. I originally picked The Haskell Road more for its relation to functional programming than to anything else. For this reason, the chapters on induction, recursion and corecursion were more enlightening and understandable than any other section. For a kid with no formal mathematical training, though, the proofs in this book (mostly those in the later chapters) were often beyond my reach.

If an exercise like the following sounds like fun, you'll enjoy this book:

Show that the relation < on N is the transitive closure of the relation R = {(n, n + 1) | n in N}.

In many chapters, the Haskell exercises are few and far between, but were (for me) a lot of fun:

Give a corecursive program for producing the Thue-Morse sequence as a stream.

[Maiz Lulkin · Rating 5 out of 5]

The most hard core programming language ever - Haskell - presented in a really different and thought provoking way. For those interested in this topics - functional languages, logics and mathematical foundations - i think it's must have.

[Joost · Rating 4 out of 5]

Didn't finish yet. Need to pick it up again at a later point in time.